Cutting out a part of a plane from sphere vertices
Here are some steps for you. (Since you'll will surely make your catapult like a solid object)

First create a Uvsphere with default options.


Now, in edit mode, Select the Top half Vertices of the Sphere.

Delete Them.

press Ctrl+A to select all the vertices , Then Press E to Extrude and immediately press ALT+S to Scale the Uvsphere. Scale it outward to get a shape like this.

Now, press Ctrl+Tab and Select "FACE" selection mode. Select the 2 faces on X axis.

Now, Simply press E to extrude and the G to move &amp; X to constrain the movement on X axis. Move it out ward. then Press S &amp; X &amp; 0 to even out the extrusion.

And , Here is a link to file 
Blend File